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Self-training is an important class of unsupervised domain adaptation (UDA) approaches that are used to mitigate the problem of domain shift, when applying knowledge learned from a labeled source domain to unlabeled and heterogeneous target domains. While self-training-based UDA has shown considerable promise on discriminative tasks, including classification and segmentation, through reliable pseudo-label filtering based on the maximum softmax probability, there is a paucity of prior work on self-training-based UDA for generative tasks, including image modality translation. To fill this gap, in this work, we seek to develop a generative self-training (GST) framework for domain adaptive image translation with continuous value prediction and regression objectives. Specifically, we quantify both aleatoric and epistemic uncertainties within our GST using variational Bayes learning to measure the reliability of synthesized data. We also introduce a self-attention scheme that de-emphasizes the background region to prevent it from dominating the training process. The adaptation is then carried out by an alternating optimization scheme with target domain supervision that focuses attention on the regions with reliable pseudo-labels. We evaluated our framework on two cross-scanner/center, inter-subject translation tasks, including tagged-to-cine magnetic resonance (MR) image translation and T1-weighted MR-to-fractional anisotropy translation. Extensive validations with unpaired target domain data showed that our GST yielded superior synthesis performance in comparison to adversarial training UDA methods. [ABSTRACT FROM AUTHOR]